An Alternative Approach To Measuring Reverberation Lags in Active Galactic Nuclei

TL;DR

This paper introduces a new statistical method for measuring reverberation lags in active galactic nuclei, improving accuracy and handling irregular data, and applies it to refine the understanding of BLR sizes and their relation to luminosity.

Contribution

The authors develop a damped random walk-based approach for directly fitting emission-line and continuum light curves, addressing limitations of traditional methods and enabling simultaneous multi-line analysis.

Findings

Redetermined lags for 87 emission lines in 31 quasars.

Confirmed the BLR size-luminosity relationship with some exceptions.

Detected the scaling of BLR size with luminosity in NGC 5548.

Abstract

Motivated by recent progress in the statistical modeling of quasar variability, we develop a new approach to measuring emission-line reverberation lags to estimate the size of broad-line regions (BLRs) in active galactic nuclei. Assuming that all emission-line light curves are scaled, smoothed, and displaced versions of the continuum, this alternative approach fits the light curves directly using a damped random walk model and aligns them to recover the time lag and its statistical confidence limits. We introduce the mathematical formalism of this approach and demonstrate its ability to cope with some of the problems for traditional methods, such as irregular sampling, correlated errors, and seasonal gaps. We redetermine the lags for 87 emission lines in 31 quasars and reassess the BLR size--luminosity relationship using 60 H-beta lags. We confirm the general results from the traditional cross-correlation methods, with a few exceptions. Our method, however, also supports a broad range of extensions. In particular, it can simultaneously fit multiple lines and continuum light curves which improves the lag estimate for the lines and provides estimates of the error correlations between them. Determining these correlations is of particular importance for interpreting emission-line velocity--delay maps. We can also include parameters for luminosity-dependent lags or line responses. We use this to detect the scaling of the BLR size with continuum luminosity in NGC 5548.